Sphericity determination using resonant ultrasound spectroscopy

Abstract

A method is provided for grading production quantities of spherical objects, such as roller balls for bearings. A resonant ultrasound spectrum (RUS) is generated for each spherical object and a set of degenerate sphere-resonance frequencies is identified. From the degenerate sphere-resonance frequencies and known relationships between degenerate sphere-resonance frequencies and Poisson's ratio, a Poisson's ratio can be determined, along with a "best" spherical diameter, to form spherical parameters for the sphere. From the RUS, fine-structure resonant frequency spectra are identified for each degenerate sphere-resonance frequency previously selected. From each fine-structure spectrum and associated sphere parameter values an asphericity value is determined. The asphericity value can then be compared with predetermined values to provide a measure for accepting or rejecting the sphere.

What is claimed is: 
     
       1. A method for grading spherical objects against predetermined values, comprising the steps of: generating a resonant ultrasound spectrum from a spherical object, where said spectrum includes a plurality of fine-structure resonant frequency spectra;   estimating from each one of said fine-structure resonant frequeny spectra a corresponding degenerate sphere-resonance frequency;   determining from said degenerate sphere-resonance frequencies of said spectrum sphere parameter values of said spherical object;   determining from said fine-structure resonant spectra of said spectrum and said sphere parameter values an asphericity value of said spherical object; and   comparing said asphericity value with said predetermined values to grade said spherical object.   
     
     
       2. A method according to claim 1, wherein the step of determining said sphere parameter values further comprises the steps of: determining a value of Poisson's ratio from said degenerate sphere-resonance frequencies; and   calculating a sphere diameter effective to produce said degenerate sphere-resonance frequencies at said determined value of Poisson's ratio.   
     
     
       3. A method according to claim 1, wherein the step of determining said asphericity value further comprises the steps of: calculating from said fine-structure resonant frequency spectra and said sphere parameter values individual asphericity values that produce the fine-structure resonant frequency spectra measure for selected degenerate sphere-resonances in said spectrum; and   averaging said individual asphericity values for each one of said selected degenerate sphere-resonances to determine said asphericity value of said spherical object.   
     
     
       4. A method according to claim 2 wherein the step of determining said asphericity value further comprises the steps of: calculating from said fine-structure resonant frequency spectra and said sphere parameter values individual asphericity values that produce the fine-structure resonant frequency spectra measure for selected degenerate sphere-resonances in said spectrum; and   average said individual asphericity values for each one of said selected degenerate sphere-resonances to determine said asphericity value of said spherical object.   
     
     
       5. A method for grading spherical objects against predetermined values, comprising the steps of: calculating a set of degenerate sphere-resonance frequencies for said object;   associating said set of degenerate sphere-resonance frequencies with a value of Poisson's ratio for said spherical object;   calculating sphere parameter values for said spherical object from said set of degenerate sphere-resonance frequencies and said value of Posson's ratio;   identifying fine-structure resonant frequency spectra associated with each degenerate sphere-resonance frequency in said set;   generating an asphericity value from each said fine structure resonant frequency spectra and said sphere parameter values; and   comparing said sphericity value and predetermined values to grade said spherical component.   
     
     
       6. A method for grading producing objects from selected object dimensions, comprising the steps of: determining by calculations a first set of resonant frequencies values as a function of Poisson's ratio for said production objects having ideal object dimensions;   determining by calculations a second set of resonant frequency values as a function of deviation of said selected production dimensions from said ideal object dimensions;   generating a resonant ultrasound spectrum from a one of said production objects, where said spectrum includes a plurality of fine-structure resonance frequency spectra;   estimating from each one of said fine-structure resonance frequency spectra a corresponding degenerate resonance frequency;   determining from said degenerate resonance frequencies resonant frequencies within said first set of resonant frequencies and corresponding values for said selected object dimensions;   determining from said fine-structure resonance frequency spectra deviation values for said corresponding object dimensions; and   grading said object from said corresponding object dimensions and said deviation values.   
     
     
       7. A method according to claim 6, wherein the step of determining said corresponding values for said selected object dimensions further comprises the steps of: determining a value of Poisson's ratio from said degenerate resonance frequencies; and   calculating said corresponding object dimensions defective to produce said degenerate resonance frequencies at said determined value of Poisson's ratio.   
     
     
       8. A method according to claim 6, wherein the step of determining said deviation values further comprises the steps of; calculating from said fine-structure resonance frequency spectra and said ideal object dimensions individual deviation values that produce said fine-structure resonance frequency spectra measured for selected resonances in said spectrum; and   averaging said individual deviation values for each one of said selected resonances to determine said deviation value for use in grading said object.